Identifying the contribution of higher $ρ$ mesons around 2 GeV in the $e^+ e^- \to ωπ^0$ and $e^+ e^- \to ρη^{\prime}$ processes

Abstract

The properties of the light vector meson states around 2.0 GeV have been poorly understood for a long time, which has become a barrier to the expansion to higher light vector meson spectrum. Recently, the BESIII collaboration released the measurements of the $e^+ e^- \to ωπ^0$ and $e^+ e^- \to ρη^{\prime}$ reactions above 2.0 GeV, both of which are ideal processes to study the isovector $ρ$ meson family. In this work, through carrying out a combined analysis of the Born cross section data for the above two processes with the theoretical support on mass spectrum, and production and strong decay behaviors of the $ρ$ meson family around 2.0 GeV, we identify the enhancement structure near 2034 MeV observed in $e^+e^-\toωπ^0$ to be the interference contribution from two resonances $ρ(1900)$ and $ρ(2150)$, and another enhancement structure at 2111 MeV reported in $e^+e^-\toρη^{\prime}$ to be the contributions from $ρ(2000)$ and $ρ(2150)$. This conclusion means that the $e^+e^-\toωπ^0$ and $e^+e^-\toρη^{\prime}$ are the excellent golden channels to establish $ρ(1900)$ and $ρ(2000)$, especially for a $D$-wave state $ρ(2000)$, whose experimental search in the $e^+e^-$ collision should be quite challenging. The relevant cross section measurements with higher precision are expected in the future BESIII and Belle II experiments.